Calculate the magnetic field inside a solenold ,when
(a) The length of the solenoid becomes twice and fixed number of turns
(b) both the length of the solenoid and number of turns are double
(c ) the number of turns becomes twice for the fixed length of the solenoid compare the results,

Explanation

The magnetic field of a solenoid (inside ) is
`B_(L.N) = mu_(0) (NI)/(L)`
(a) length of the solenoid becomes twice and fixed number of turns
L `rarr`2L (length becomes twice )
N `rarr` N(number of turns are fixed )
The magnetic field is
`B_(2 L,N) = mu_(0) (NI)/(2L) = (1)/(2) B_(L,N)`
(b) both the length of the solenoid and number of turns are double
L `rarr` 2L (length becomes twice )
N `rarr` 2N ( number of turns becomes twice )
The magnetic field is
`B_(2L,2N) = mu_(0) (2NI)/(2L) = B_(L,N)`
( c) the number of turns becomes twice but for the fixed lenght of the solenoid .
L `rarr` L (length is fixed ) N `rarr` 2N ( number of turns becomes twices )
the magnetic field is `B_(L,2N) = mu_(0) (2NI)/(L) = 2B_(L,N)`
From the above results ,
`B_(2L,2N) gt B_(2L,2N) gt B_(2L,N)`
Thus, strength of the magnetic field is increased when we pack more loops into the same length for a given current.